MAYBE

Problem:
 from(X) -> cons(X,n__from(n__s(X)))
 sel(0(),cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   sel#(s(X),cons(Y,Z)) -> activate#(Z)
   sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   from(X) -> cons(X,n__from(n__s(X)))
   sel(0(),cons(X,Y)) -> X
   sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
   TRS:
    f12(x,y) -> x
    f12(x,y) -> y
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
    from(X) -> cons(X,n__from(n__s(X)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
   CDG Processor:
    DPs:
     sel#(s(X),cons(Y,Z)) -> activate#(Z)
     sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
     activate#(n__from(X)) -> activate#(X)
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> s#(activate(X))
    TRS:
     f12(x,y) -> x
     f12(x,y) -> y
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
     from(X) -> cons(X,n__from(n__s(X)))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
    graph:
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__from(X)) -> activate#(X)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__s(X)) -> activate#(X)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__from(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__s(X)) -> s#(activate(X))
     sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
     activate#(n__from(X)) -> activate#(X)
     sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
     activate#(n__from(X)) -> from#(activate(X))
     sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
     activate#(n__s(X)) -> activate#(X)
     sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
     activate#(n__s(X)) -> s#(activate(X))
     sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) ->
     sel#(s(X),cons(Y,Z)) -> activate#(Z)
     sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) -> sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
    Restore Modifier:
     DPs:
      sel#(s(X),cons(Y,Z)) -> activate#(Z)
      sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
      activate#(n__from(X)) -> activate#(X)
      activate#(n__from(X)) -> from#(activate(X))
      activate#(n__s(X)) -> activate#(X)
      activate#(n__s(X)) -> s#(activate(X))
     TRS:
      from(X) -> cons(X,n__from(n__s(X)))
      sel(0(),cons(X,Y)) -> X
      sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
      from(X) -> n__from(X)
      s(X) -> n__s(X)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(X) -> X
     SCC Processor:
      #sccs: 2
      #rules: 3
      #arcs: 14/36
      DPs:
       sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
      TRS:
       from(X) -> cons(X,n__from(n__s(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
       from(X) -> n__from(X)
       s(X) -> n__s(X)
       activate(n__from(X)) -> from(activate(X))
       activate(n__s(X)) -> s(activate(X))
       activate(X) -> X
      Open
      
      DPs:
       activate#(n__from(X)) -> activate#(X)
       activate#(n__s(X)) -> activate#(X)
      TRS:
       from(X) -> cons(X,n__from(n__s(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
       from(X) -> n__from(X)
       s(X) -> n__s(X)
       activate(n__from(X)) -> from(activate(X))
       activate(n__s(X)) -> s(activate(X))
       activate(X) -> X
      Open